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arXiv · 2509.22597

Nonparametric Bayesian Calibration of Computer Models

Haiyi Shi·Lei Yang·Jiarui Chi·Derek Bingham·Troy Butler·Don Estep·Haonan Wang
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Abstract

Combining field data and computer models is a crucial step for making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for calibrating the distribution of parameters in a computer model using field observations. Our results include establishing; a unique nonparametric Bayesian posterior corresponding to a chosen prior with an explicit formula for the posterior density; a maximum entropy property of the posterior corresponding to the uniform prior; the almost everywhere continuity of the posterior density; and a comprehensive statistical analysis of an estimator based on importance sampling. They also include establishing the well-posedness of the nonparametric Bayesian solution of the calibration problem. We illustrate the results using several examples.

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Haiyi Shi, Lei Yang, Jiarui Chi, Derek Bingham, Troy Butler, Don Estep, Haonan Wang. 2025-09-26. Nonparametric Bayesian Calibration of Computer Models. https://arxiv.org/abs/2509.22597

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